4. Definition of Infinite Limit: Let X CR, f: X R and a e X'. If for every M > 0 there exists o > 0 such that |f(r)| > M whenever r EX and 0 < |r - al < 6 then we say that the limit as r approaches a of f(x) is oo which is denoted as lim f(r) = o. Suppose a € R, e > 0, and f, g : N*(a, e) → R. If lim f (x) = L > 0 and lim g(x) = 0, prove lim(fg)(x) = 00 %3D エ→a 全→a エ→a
4. Definition of Infinite Limit: Let X CR, f: X R and a e X'. If for every M > 0 there exists o > 0 such that |f(r)| > M whenever r EX and 0 < |r - al < 6 then we say that the limit as r approaches a of f(x) is oo which is denoted as lim f(r) = o. Suppose a € R, e > 0, and f, g : N*(a, e) → R. If lim f (x) = L > 0 and lim g(x) = 0, prove lim(fg)(x) = 00 %3D エ→a 全→a エ→a
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:4. Definition of Infinite Limit: Let XCR, f: X R and a e X'. If for every M > 0
there exists o > 0 such that |f(r)| > M whenever r € X and 0 < |r - al < 6 then we
say that the limit as r approaches a of f(x) is o which is denoted as lim f(x) = 00.
Suppose a € R, e > 0, and f, g : N*(a, e) → R. If lim f (x) = L > 0 and lim g(x) = 00,
エ→a
prove lim(fg)(x) = 00
エ→a
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